Vector Data
An introduction to simple features
names(world)
[1] "iso_a2" "name_long" "continent" "region_un" "subregion"
[6] "type" "area_km2" "pop" "lifeExp" "gdpPercap"
[11] "geom"
world
Simple feature collection with 177 features and 10 fields
geometry type: MULTIPOLYGON
dimension: XY
bbox: xmin: -180 ymin: -90 xmax: 180 ymax: 83.64513
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
plot(world, max.plot = 10)

summary(world["lifeExp"])
lifeExp geom
Min. :50.62 MULTIPOLYGON :177
1st Qu.:64.96 epsg:4326 : 0
Median :72.87 +proj=long...: 0
Mean :70.85
3rd Qu.:76.78
Max. :83.59
NA's :10
world$geom[[1]]
MULTIPOLYGON (((180 -16.06713, 180 -16.55522, 179.3641 -16.80135, 178.7251 -17.01204, 178.5968 -16.63915, 179.0966 -16.43398, 179.4135 -16.37905, 180 -16.06713)), ((178.1256 -17.50481, 178.3736 -17.33992, 178.7181 -17.62846, 178.5527 -18.15059, 177.9327 -18.28799, 177.3815 -18.16432, 177.285 -17.72465, 177.6709 -17.38114, 178.1256 -17.50481)), ((-179.7933 -16.02088, -179.9174 -16.50178, -180 -16.55522, -180 -16.06713, -179.7933 -16.02088)))
world_mini = world[1:2, 1:3]
world_mini
Simple feature collection with 2 features and 3 fields
geometry type: MULTIPOLYGON
dimension: XY
bbox: xmin: -180 ymin: -18.28799 xmax: 180 ymax: -0.95
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
library(sp)
world_sp = as(world, Class = "Spatial")
world_sp
class : SpatialPolygonsDataFrame
features : 177
extent : -180, 180, -90, 83.64513 (xmin, xmax, ymin, ymax)
crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
variables : 10
names : iso_a2, name_long, continent, region_un, subregion, type, area_km2, pop, lifeExp, gdpPercap
min values : AE, Afghanistan, Africa, Africa, Antarctica, Country, 2416.87048266498, 56295, 50.621, 597.135168986395
max values : ZW, Zimbabwe, South America, Seven seas (open ocean), Western Europe, Sovereign country, 17018507.4094666, 1364270000, 83.5878048780488, 120860.06755829
world_sf = st_as_sf(world_sp)
world_sf
Simple feature collection with 177 features and 10 fields
geometry type: MULTIPOLYGON
dimension: XY
bbox: xmin: -180 ymin: -90 xmax: 180 ymax: 83.64513
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
First 10 features:
iso_a2 name_long continent region_un subregion
1 FJ Fiji Oceania Oceania Melanesia
2 TZ Tanzania Africa Africa Eastern Africa
3 EH Western Sahara Africa Africa Northern Africa
4 CA Canada North America Americas Northern America
5 US United States North America Americas Northern America
6 KZ Kazakhstan Asia Asia Central Asia
7 UZ Uzbekistan Asia Asia Central Asia
8 PG Papua New Guinea Oceania Oceania Melanesia
9 ID Indonesia Asia Asia South-Eastern Asia
10 AR Argentina South America Americas South America
type area_km2 pop lifeExp gdpPercap
1 Sovereign country 19289.97 885806 69.96000 8222.254
2 Sovereign country 932745.79 52234869 64.16300 2402.099
3 Indeterminate 96270.60 NA NA NA
4 Sovereign country 10036042.98 35535348 81.95305 43079.143
5 Country 9510743.74 318622525 78.84146 51921.985
6 Sovereign country 2729810.51 17288285 71.62000 23587.338
7 Sovereign country 461410.26 30757700 71.03900 5370.866
8 Sovereign country 464520.07 7755785 65.23000 3709.082
9 Sovereign country 1819251.33 255131116 68.85600 10003.089
10 Sovereign country 2784468.59 42981515 76.25200 18797.548
geometry
1 MULTIPOLYGON (((180 -16.067...
2 MULTIPOLYGON (((33.90371 -0...
3 MULTIPOLYGON (((-8.66559 27...
4 MULTIPOLYGON (((-122.84 49,...
5 MULTIPOLYGON (((-122.84 49,...
6 MULTIPOLYGON (((87.35997 49...
7 MULTIPOLYGON (((55.96819 41...
8 MULTIPOLYGON (((141.0002 -2...
9 MULTIPOLYGON (((141.0002 -2...
10 MULTIPOLYGON (((-68.63401 -...
Basic map making
plot(world[3:6])

plot(world["pop"])

world_asia <- world %>%
filter(continent == "Asia")
world_asia
Simple feature collection with 47 features and 10 fields
geometry type: MULTIPOLYGON
dimension: XY
bbox: xmin: 26.04335 ymin: -10.35999 xmax: 145.5431 ymax: 55.38525
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
asia = st_union(world_asia)
asia
Geometry set for 1 feature
geometry type: MULTIPOLYGON
dimension: XY
bbox: xmin: 26.04335 ymin: -10.35999 xmax: 145.5431 ymax: 55.38525
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
MULTIPOLYGON (((120.295 -10.25865, 118.9678 -9....
plot(world["pop"], reset = FALSE)
plot(asia, add = TRUE, col = "red")

plot(world["continent"], reset = FALSE)
cex = sqrt(world$pop) / 10000
world_cents = st_centroid(world, of_largest = TRUE)
st_centroid assumes attributes are constant over geometries of xst_centroid does not give correct centroids for longitude/latitude data
plot(st_geometry(world_cents), add = TRUE, cex = cex)

india = world[world$name_long == "India", ]
plot(st_geometry(india), expandBB = c(0, 0.2, 0.1, 1), col = "gray", lwd = 3)
plot(world_asia[0], add = TRUE)

Geometry tyeps
Simple feature geometries (sfg)
st_point(c(5, 2)) # XY point
POINT (5 2)
st_point(c(5, 2, 3)) # XYZ point
POINT Z (5 2 3)
st_point(c(5, 2, 1), dim = "XYM") # XYM point
POINT M (5 2 1)
st_point(c(5, 2, 3, 1)) # XYZM point
POINT ZM (5 2 3 1)
# the rbind function simplifies the creation of matrices
## MULTIPOINT
multipoint_matrix = rbind(c(5, 2), c(1, 3), c(3, 4), c(3, 2))
st_multipoint(multipoint_matrix)
MULTIPOINT (5 2, 1 3, 3 4, 3 2)
## LINESTRING
linestring_matrix = rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2))
st_linestring(linestring_matrix)
LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)
## POLYGON
polygon_list = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)))
st_polygon(polygon_list)
POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5))
## POLYGON with a hole
polygon_border = rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))
polygon_hole = rbind(c(2, 4), c(3, 4), c(3, 3), c(2, 3), c(2, 4))
polygon_with_hole_list = list(polygon_border, polygon_hole)
st_polygon(polygon_with_hole_list)
POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5), (2 4, 3 4, 3 3, 2 3, 2 4))
## MULTILINESTRING
multilinestring_list = list(
rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)),
rbind(c(1, 2), c(2, 4))
)
st_multilinestring((multilinestring_list))
MULTILINESTRING ((1 5, 4 4, 4 1, 2 2, 3 2), (1 2, 2 4))
## MULTIPOLYGON
multipolygon_list = list(
list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))),
list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2)))
)
st_multipolygon(multipolygon_list)
MULTIPOLYGON (((1 5, 2 2, 4 1, 4 4, 1 5)), ((0 2, 1 2, 1 3, 0 3, 0 2)))
## GEOMETRYCOLLECTION
gemetrycollection_list = list(st_multipoint(multipoint_matrix),
st_linestring(linestring_matrix))
st_geometrycollection(gemetrycollection_list)
GEOMETRYCOLLECTION (MULTIPOINT (5 2, 1 3, 3 4, 3 2), LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2))
Simple feature columns (sfc)
# sfc POINT
point1 = st_point(c(5, 2))
point2 = st_point(c(1, 3))
points_sfc = st_sfc(point1, point2)
points_sfc
Geometry set for 2 features
geometry type: POINT
dimension: XY
bbox: xmin: 1 ymin: 2 xmax: 5 ymax: 3
epsg (SRID): NA
proj4string: NA
POINT (5 2)
POINT (1 3)
# sfc POLYGON
polygon_list1 = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)))
polygon1 = st_polygon(polygon_list1)
polygon_list2 = list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2)))
polygon2 = st_polygon(polygon_list2)
polygon_sfc = st_sfc(polygon1, polygon2)
polygon_sfc
Geometry set for 2 features
geometry type: POLYGON
dimension: XY
bbox: xmin: 0 ymin: 1 xmax: 4 ymax: 5
epsg (SRID): NA
proj4string: NA
POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5))
POLYGON ((0 2, 1 2, 1 3, 0 3, 0 2))
# sfc MULTILINESTRING
multilinestring_list1 = list(
rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)),
rbind(c(1, 2), c(2, 4))
)
multilinestring1 = st_multilinestring((multilinestring_list1))
multilinestring_list2 = list(
rbind(c(2, 9), c(7, 9), c(5, 6), c(4, 7), c(2, 7)),
rbind(c(1, 7), c(3, 8))
)
multilinestring2 = st_multilinestring((multilinestring_list2))
multilinestring_sfc = st_sfc(multilinestring1, multilinestring2)
multilinestring_sfc
Geometry set for 2 features
geometry type: MULTILINESTRING
dimension: XY
bbox: xmin: 1 ymin: 1 xmax: 7 ymax: 9
epsg (SRID): NA
proj4string: NA
MULTILINESTRING ((1 5, 4 4, 4 1, 2 2, 3 2), (1 ...
MULTILINESTRING ((2 9, 7 9, 5 6, 4 7, 2 7), (1 ...
# sfc GEOMETRY
point_multilinestring_sfc = st_sfc(point1, multilinestring1)
point_multilinestring_sfc
Geometry set for 2 features
geometry type: GEOMETRY
dimension: XY
bbox: xmin: 1 ymin: 1 xmax: 5 ymax: 5
epsg (SRID): NA
proj4string: NA
POINT (5 2)
MULTILINESTRING ((1 5, 4 4, 4 1, 2 2, 3 2), (1 ...
points_sfc
Geometry set for 2 features
geometry type: POINT
dimension: XY
bbox: xmin: 1 ymin: 2 xmax: 5 ymax: 3
epsg (SRID): NA
proj4string: NA
POINT (5 2)
POINT (1 3)
st_crs(points_sfc)
Coordinate Reference System: NA
# EPSG definition
st_sfc(point1, point2, crs = 4326)
Geometry set for 2 features
geometry type: POINT
dimension: XY
bbox: xmin: 1 ymin: 2 xmax: 5 ymax: 3
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
POINT (5 2)
POINT (1 3)
# PROJ4STRING definition
st_sfc(point1, point2, crs = "+proj=longlat +datum=WGS84 +no_defs")
Geometry set for 2 features
geometry type: POINT
dimension: XY
bbox: xmin: 1 ymin: 2 xmax: 5 ymax: 3
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
POINT (5 2)
POINT (1 3)
The sf class
lnd_point = st_point(c(0.1, 51.5)) # sfg object
lnd_geom = st_sfc(lnd_point, crs = 4326) # sfc object
lnd_attrib = data.frame( # data.frame object
name = "London",
temperature = 25,
date = as.Date("2017-06-21")
)
lnd_sf = st_sf(lnd_attrib, geometry = lnd_geom) # sf object
lnd_sf
Simple feature collection with 1 feature and 3 fields
geometry type: POINT
dimension: XY
bbox: xmin: 0.1 ymin: 51.5 xmax: 0.1 ymax: 51.5
epsg (SRID): 4326
proj4string: +proj=longlat +datum=WGS84 +no_defs
name temperature date geometry
1 London 25 2017-06-21 POINT (0.1 51.5)
class(lnd_sf)
[1] "sf" "data.frame"
Raster data
An introduction to raster
new_raster
class : RasterLayer
dimensions : 457, 465, 212505 (nrow, ncol, ncell)
resolution : 0.0008333333, 0.0008333333 (x, y)
extent : -113.2396, -112.8521, 37.13208, 37.51292 (xmin, xmax, ymin, ymax)
crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
source : /Library/Frameworks/R.framework/Versions/3.6/Resources/library/spDataLarge/raster/srtm.tif
names : srtm
values : 1024, 2892 (min, max)
dim(new_raster)
[1] 457 465 1
ncell(new_raster)
[1] 212505
res(new_raster)
[1] 0.0008333333 0.0008333333
extent(new_raster)
class : Extent
xmin : -113.2396
xmax : -112.8521
ymin : 37.13208
ymax : 37.51292
crs(new_raster)
CRS arguments:
+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
inMemory(new_raster)
[1] FALSE
Basic map making

Raster clsses

raster::writeFormats()
name long_name
[1,] "raster" "R-raster"
[2,] "SAGA" "SAGA GIS"
[3,] "IDRISI" "IDRISI"
[4,] "IDRISIold" "IDRISI (img/doc)"
[5,] "BIL" "Band by Line"
[6,] "BSQ" "Band Sequential"
[7,] "BIP" "Band by Pixel"
[8,] "ascii" "Arc ASCII"
[9,] "CDF" "NetCDF"
[10,] "big" "big.matrix"
[11,] "ADRG" "ARC Digitized Raster Graphics"
[12,] "BMP" "MS Windows Device Independent Bitmap"
[13,] "BT" "VTP .bt (Binary Terrain) 1.3 Format"
[14,] "BYN" "Natural Resources Canada's Geoid"
[15,] "CTable2" "CTable2 Datum Grid Shift"
[16,] "EHdr" "ESRI .hdr Labelled"
[17,] "ELAS" "ELAS"
[18,] "ENVI" "ENVI .hdr Labelled"
[19,] "ERS" "ERMapper .ers Labelled"
[20,] "GPKG" "GeoPackage"
[21,] "GS7BG" "Golden Software 7 Binary Grid (.grd)"
[22,] "GSBG" "Golden Software Binary Grid (.grd)"
[23,] "GTiff" "GeoTIFF"
[24,] "GTX" "NOAA Vertical Datum .GTX"
[25,] "HFA" "Erdas Imagine Images (.img)"
[26,] "IDA" "Image Data and Analysis"
[27,] "ILWIS" "ILWIS Raster Map"
[28,] "INGR" "Intergraph Raster"
[29,] "ISCE" "ISCE raster"
[30,] "ISIS2" "USGS Astrogeology ISIS cube (Version 2)"
[31,] "ISIS3" "USGS Astrogeology ISIS cube (Version 3)"
[32,] "KRO" "KOLOR Raw"
[33,] "LAN" "Erdas .LAN/.GIS"
[34,] "Leveller" "Leveller heightfield"
[35,] "MBTiles" "MBTiles"
[36,] "MRF" "Meta Raster Format"
[37,] "netCDF" "Network Common Data Format"
[38,] "NGW" "NextGIS Web"
[39,] "NITF" "National Imagery Transmission Format"
[40,] "NTv2" "NTv2 Datum Grid Shift"
[41,] "NWT_GRD" "Northwood Numeric Grid Format .grd/.tab"
[42,] "PAux" "PCI .aux Labelled"
[43,] "PCIDSK" "PCIDSK Database File"
[44,] "PCRaster" "PCRaster Raster File"
[45,] "PDF" "Geospatial PDF"
[46,] "PDS4" "NASA Planetary Data System 4"
[47,] "PNM" "Portable Pixmap Format (netpbm)"
[48,] "RMF" "Raster Matrix Format"
[49,] "ROI_PAC" "ROI_PAC raster"
[50,] "RRASTER" "R Raster"
[51,] "RST" "Idrisi Raster A.1"
[52,] "SAGA" "SAGA GIS Binary Grid (.sdat, .sg-grd-z)"
[53,] "SGI" "SGI Image File Format 1.0"
[54,] "Terragen" "Terragen heightfield"

r_brick
class : RasterBrick
dimensions : 1428, 1128, 1610784, 4 (nrow, ncol, ncell, nlayers)
resolution : 30, 30 (x, y)
extent : 301905, 335745, 4111245, 4154085 (xmin, xmax, ymin, ymax)
crs : +proj=utm +zone=12 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0
source : /Library/Frameworks/R.framework/Versions/3.6/Resources/library/spDataLarge/raster/landsat.tif
names : landsat.1, landsat.2, landsat.3, landsat.4
min values : 7550, 6404, 5678, 5252
max values : 19071, 22051, 25780, 31961
nlayers(r_brick)
[1] 4
plot(r_brick)

raster_on_disk = raster(r_brick, layer = 1)
plot(raster_on_disk)

raster_in_memory = raster(xmn = 301905, xmx = 335745,
ymn = 4111245, ymx = 4154085,
res = 30)
values(raster_in_memory) = sample(seq_len(ncell(raster_in_memory)))
crs(raster_in_memory) = crs(raster_on_disk)
plot(raster_in_memory)

r_stack = stack(raster_in_memory, raster_on_disk)
r_stack
class : RasterStack
dimensions : 1428, 1128, 1610784, 2 (nrow, ncol, ncell, nlayers)
resolution : 30, 30 (x, y)
extent : 301905, 335745, 4111245, 4154085 (xmin, xmax, ymin, ymax)
crs : +proj=utm +zone=12 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0
names : layer, landsat.1
min values : 1, 7550
max values : 1610784, 19071

---
title: "R Notebook"
output:
  html_notebook: default
  word_document: default
---

```{r}
library(tidyverse)
library(sf)
library(raster)
library(spData)
library(spDataLarge)
library(lwgeom)

knitr::opts_chunk$set()
```

# Vector Data

## An introduction to simple features

```{r}
names(world)
```

```{r}
world
```

```{r}
plot(world, max.plot = 10)
```

```{r}
summary(world["lifeExp"])
```

```{r}
world$geom[[1]]
```

```{r}
world_mini = world[1:2, 1:3]
world_mini
```

```{r}
library(sp)
world_sp = as(world, Class = "Spatial")
world_sp
world_sf = st_as_sf(world_sp)
world_sf
```

## Basic map making

```{r}
plot(world[3:6])
```

```{r}
plot(world["pop"])
```


```{r}
world_asia <- world %>% 
  filter(continent == "Asia")
world_asia
```

```{r}
asia = st_union(world_asia)
asia
```

```{r}
plot(world["pop"], reset = FALSE)
plot(asia, add = TRUE, col = "red")
```

```{r}
plot(world["continent"], reset = FALSE)
cex = sqrt(world$pop) / 10000
world_cents = st_centroid(world, of_largest = TRUE)
plot(st_geometry(world_cents), add = TRUE, cex = cex)
```

```{r}
india = world[world$name_long == "India", ]
plot(st_geometry(india), expandBB = c(0, 0.2, 0.1, 1), col = "gray", lwd = 3)
plot(world_asia[0], add = TRUE)
```

## Geometry tyeps

## Simple feature geometries (sfg)



```{r}
st_point(c(5, 2))                 # XY point
st_point(c(5, 2, 3))              # XYZ point
st_point(c(5, 2, 1), dim = "XYM") # XYM point
st_point(c(5, 2, 3, 1))           # XYZM point
```

```{r}
# the rbind function simplifies the creation of matrices

## MULTIPOINT
multipoint_matrix = rbind(c(5, 2), c(1, 3), c(3, 4), c(3, 2))
st_multipoint(multipoint_matrix)

## LINESTRING
linestring_matrix = rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2))
st_linestring(linestring_matrix)
```

```{r}
## POLYGON
polygon_list = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)))
st_polygon(polygon_list)
```

```{r}
## POLYGON with a hole
polygon_border = rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))
polygon_hole = rbind(c(2, 4), c(3, 4), c(3, 3), c(2, 3), c(2, 4))
polygon_with_hole_list = list(polygon_border, polygon_hole)
st_polygon(polygon_with_hole_list)
```

```{r}
## MULTILINESTRING
multilinestring_list = list(
  rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)), 
  rbind(c(1, 2), c(2, 4))
  )
st_multilinestring((multilinestring_list))
```

```{r}
## MULTIPOLYGON
multipolygon_list = list(
  list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))),
  list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2)))
  )
st_multipolygon(multipolygon_list)
```

```{r}
## GEOMETRYCOLLECTION
gemetrycollection_list = list(st_multipoint(multipoint_matrix),
                              st_linestring(linestring_matrix))
st_geometrycollection(gemetrycollection_list)
```

## Simple feature columns (sfc)

```{r}
# sfc POINT
point1 = st_point(c(5, 2))
point2 = st_point(c(1, 3))
points_sfc = st_sfc(point1, point2)
points_sfc
```

```{r}
# sfc POLYGON
polygon_list1 = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)))
polygon1 = st_polygon(polygon_list1)

polygon_list2 = list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2)))
polygon2 = st_polygon(polygon_list2)

polygon_sfc = st_sfc(polygon1, polygon2)
polygon_sfc
```

```{r}
# sfc MULTILINESTRING
multilinestring_list1 = list(
  rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)), 
  rbind(c(1, 2), c(2, 4))
  )
multilinestring1 = st_multilinestring((multilinestring_list1))

multilinestring_list2 = list(
  rbind(c(2, 9), c(7, 9), c(5, 6), c(4, 7), c(2, 7)), 
  rbind(c(1, 7), c(3, 8))
  )
multilinestring2 = st_multilinestring((multilinestring_list2))

multilinestring_sfc = st_sfc(multilinestring1, multilinestring2)
multilinestring_sfc
```

```{r}
# sfc GEOMETRY
point_multilinestring_sfc = st_sfc(point1, multilinestring1)
point_multilinestring_sfc
```

```{r}
points_sfc
```

```{r}
st_crs(points_sfc)
```

```{r}
# EPSG definition
st_sfc(point1, point2, crs = 4326)
```

```{r}
# PROJ4STRING definition
st_sfc(point1, point2, crs = "+proj=longlat +datum=WGS84 +no_defs")
```

## The sf class

```{r}
lnd_point = st_point(c(0.1, 51.5))                 # sfg object
lnd_geom = st_sfc(lnd_point, crs = 4326)           # sfc object
lnd_attrib = data.frame(                           # data.frame object
  name = "London",
  temperature = 25,
  date = as.Date("2017-06-21")
  )
lnd_sf = st_sf(lnd_attrib, geometry = lnd_geom)    # sf object
lnd_sf
```

```{r}
class(lnd_sf)
```

# Raster data

## An introduction to raster

```{r}
raster_filepath = system.file("raster/srtm.tif", package = "spDataLarge")
new_raster = raster(raster_filepath)
new_raster
```

```{r}
dim(new_raster)
```

```{r}
ncell(new_raster)
```

```{r}
res(new_raster)
```

```{r}
extent(new_raster)
```

```{r}
crs(new_raster)
```

```{r}
inMemory(new_raster)
```

## Basic map making

```{r}
plot(new_raster)
```

## Raster clsses

```{r}
raster_filepath = system.file("raster/srtm.tif", package = "spDataLarge")
new_raster = raster(raster_filepath)
plot(new_raster)
```

```{r}
raster::writeFormats()
```

```{r}
rgdal::gdalDrivers()
```



```{r}
new_raster2 = raster(nrows = 6, ncols = 6, res = 0.5, 
                     xmn = -1.5, xmx = 1.5, ymn = -1.5, ymx = 1.5,
                     vals = 1:36)
plot(new_raster2)
```

```{r}
multi_raster_file = system.file("raster/landsat.tif", package = "spDataLarge")
r_brick = brick(multi_raster_file)
r_brick
```

```{r}
nlayers(r_brick)
```

```{r}
plot(r_brick)
```


```{r}
raster_on_disk = raster(r_brick, layer = 1)
plot(raster_on_disk)
```

```{r}
raster_in_memory = raster(xmn = 301905, xmx = 335745,
                          ymn = 4111245, ymx = 4154085, 
                          res = 30)
values(raster_in_memory) = sample(seq_len(ncell(raster_in_memory)))
crs(raster_in_memory) = crs(raster_on_disk)
plot(raster_in_memory)
```


```{r}
r_stack = stack(raster_in_memory, raster_on_disk)
r_stack
```

```{r}
plot(r_stack)
```


# Coordinate Reference System

## Geographic coordinate system

## Projected coordinate reference systems

## CRS in R

```{r}
rgdal::make_EPSG()
```

```{r}
vector_filepath = system.file("vector/zion.gpkg", package = "spDataLarge")
new_vector = st_read(vector_filepath)
```

```{r}
st_crs(new_vector)
```

```{r}
new_vector = st_set_crs(new_vector, 4326) # set CRS
```

```{r}
projection(new_raster) # get CRS
```

```{r}
projection(new_raster) = "+proj=utm +zone=12 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs" # set CRS
```

```{r}
plot(new_raster)
```

# Units

```{r}
luxembourg = world[world$name_long == "Luxembourg", ]
st_area(luxembourg)
```

```{r}
st_area(luxembourg) / 1000000
```

```{r}
units::set_units(st_area(luxembourg), km^2)
```

```{r}
res(new_raster)
```

```{r}
repr = projectRaster(new_raster, crs = "+init=epsg:26912")
res(repr)
```

